The document is an overview of the EE 324 course on feedback and control systems, covering essential concepts like open-loop and closed-loop systems, transient and steady-state responses, and system stability. It emphasizes the importance of performance analysis and design objectives, detailing how to achieve desired responses in control systems. The document also discusses the implications of system instability and the need for careful design to maintain stability and performance.

1. EE 324: FEEDBACK AND
CONTROL SYSTEM
BY: ENGR JBB

2. INTRODUCTION
• COURSE CODE: EE 324
• COURSE TITLE: FEEDBACK AND CONTROL SYSTEM
• CREDIT UNITS: 3 UNITS
• PRE-REQUISITE: ADVANCE ENGINEERING MATH FOR EE,
ELECTRONICS CIRCUITS: DEVICES AND ANALYSIS

3. • COURSE DESCRIPTION: THIS COURSE DEALS WITH THE BASICS OF CONTROL
SYSTEMS; TERMINOLOGIES AND DIAGRAMS; HOMOGENEOUS AND TRANSIENT
RESPONSES OF SYSTEMS; SYSTEMS REPRESENTATION SUCH AS TRANSFER
FUNCTIONS, STATE-SPACE ANALYSIS OF PHASE VARIABLES AND TECHNIQUES, NTH
ORDER LINEAR DIFFERENTIAL EQUATIONS; MODELING, POLE-ZERO GAIN DATA AND
FREQUENCY RESPONSE DATA; LAPLACE TRANSFORMS; BLOCK DIAGRAMS
INTERCONNECTIONS AND SIMPLIFICATIONS; SIGNAL FLOW GRAPHS; CONVERSION
OF BLOCK DIAGRAMS TO SIGNAL FLOW GRAPHS AND VICE VERSA; ROOT LOCUS;
BODE, NYQUIST AND POLAR PLOTS; PID CONTROLLERS; SENSITIVITY AND STABILITY
CRITERIA; LINEAR FEEDBACK SYSTEMS; AND COMPENSATION TECHNIQUES.

4. CONTROL SYSTEM DEFINITION
• A CONTROL SYSTEM CONSISTS OF SUBSYSTEMS AND PROCESSES (OR
PLANTS) ASSEMBLED FOR THE PURPOSE OF OBTAINING A DESIRED OUTPUT
WITH DESIRED PERFORMANCE, GIVEN A SPECIFIED INPUT. FIGURE 1.1
SHOWS A CONTROL SYSTEM IN ITS SIMPLEST FORM, WHERE THE INPUT
REPRESENTS A DESIRED OUTPUT.

5. TWO MAJOR MEASURES OF PERFORMANCE ARE APPARENT:
• (1) THE TRANSIENT RESPONSE AND
• (2) THE STEADY-STATE ERROR.
IN OUR EXAMPLE, PASSENGER COMFORT AND PASSENGER PATIENCE ARE
DEPENDENT UPON THE TRANSIENT RESPONSE. IF THIS RESPONSE IS TOO
FAST, PASSENGER COMFORT IS SACRIFICED; IF TOO SLOW, PASSENGER
PATIENCE IS SACRIFICED. THE STEADY-STATE ERROR IS ANOTHER IMPORTANT
PERFORMANCE SPECIFICATION SINCE PASSENGER SAFETY AND
CONVENIENCE WOULD BE SACRIFICED IF THE ELEVATOR DID NOT LEVEL
PROPERLY.

6. WE BUILD CONTROL SYSTEMS FOR FOUR PRIMARY
REASONS:
1. POWER AMPLIFICATION
2. REMOTE CONTROL
3. CONVENIENCE OF INPUT FORM
4. COMPENSATION FOR DISTURBANCES

7. SYSTEM CONFIGURATIONS
• OPEN-LOOP SYSTEMS A GENERIC OPEN-LOOP SYSTEM IS SHOWN IN FIGURE 1.5(A). IT STARTS WITH
A SUBSYSTEM CALLED AN INPUT TRANSDUCER, WHICH CONVERTS THE FORM OF THE INPUT TO THAT
USED BY THE CONTROLLER. THE CONTROLLER DRIVES A PROCESS OR A PLANT. THE INPUT IS
SOMETIMES CALLED THE REFERENCE, WHILE THE OUTPUT CAN BE CALLED THE CONTROLLED VARIABLE.
OTHER SIGNALS, SUCH AS DISTURBANCES, ARE SHOWN ADDED TO THE CONTROLLER AND PROCESS
OUTPUTS VIA SUMMING JUNCTIONS, WHICH YIELD THE ALGEBRAIC SUM OF THEIR INPUT SIGNALS
USING ASSOCIATED SIGNS. FOR EXAMPLE, THE PLANT CAN BE A FURNACE OR AIR CONDITIONING
SYSTEM, WHERE THE OUTPUT VARIABLE IS TEMPERATURE. THE CONTROLLER IN A HEATING SYSTEM
CONSISTS OF FUEL VALVES AND THE ELECTRICAL SYSTEM THAT OPERATES THE VALVES.

8. SYSTEM CONFIGURATIONS

9. SYSTEM CONFIGURATIONS
• CLOSED-LOOP (FEEDBACK CONTROL) SYSTEMS THE DISADVANTAGES OF OPEN-LOOP SYSTEMS, NAMELY
SENSITIVITY TO DISTURBANCES AND INABILITY TO CORRECT FOR THESE DISTURBANCES, MAY BE OVERCOME
IN CLOSED-LOOP SYSTEMS. THE GENERIC ARCHITECTURE OF A CLOSED-LOOP SYSTEM IS SHOWN IN FIGURE
1.5(B). THE INPUT TRANSDUCER CONVERTS THE FORM OF THE INPUT TO THE FORM USED BY THE
CONTROLLER. AN OUTPUT TRANSDUCER, OR SENSOR, MEASURES THE OUTPUT RESPONSE AND CONVERTS
IT INTO THE FORM USED BY THE CONTROLLER. FOR EXAMPLE, IF THE CONTROLLER USES ELECTRICAL
SIGNALS TO OPERATE THE VALVES OF A TEMPERATURE CONTROL SYSTEM, THE INPUT POSITION AND THE
OUTPUT TEMPERATURE ARE CONVERTED TO ELECTRICAL SIGNALS. THE INPUT POSITION CAN BE CONVERTED
TO A VOLTAGE BY A POTENTIOMETER, A VARIABLE RESISTOR, AND THE OUTPUT TEMPERATURE CAN BE
CONVERTED TO A VOLTAGE BY A THERMISTOR, A DEVICE WHOSE ELECTRICAL RESISTANCE CHANGES WITH
TEMPERATURE.

10. SYSTEM CONFIGURATIONS

11. ANALYSIS AND DESIGN OBJECTIVES
• ANALYSIS IS THE PROCESS BY WHICH A SYSTEM’S PERFORMANCE IS DETERMINED. FOR EXAMPLE, WE
EVALUATE ITS TRANSIENT RESPONSE AND STEADY-STATE ERROR TO DETERMINE IF THEY MEET THE DESIRED
SPECIFICATIONS. DESIGN IS THE PROCESS BY WHICH A SYSTEM’S PERFORMANCE IS CREATED OR
CHANGED. FOR EXAMPLE, IF A SYSTEM’S TRANSIENT RESPONSE AND STEADY-STATE ERROR ARE ANALYZED
AND FOUND NOT TO MEET THE SPECIFICATIONS, THEN WE CHANGE PARAMETERS OR ADD ADDITIONAL
COMPONENTS TO MEET THE SPECIFICATIONS.
• A CONTROL SYSTEM IS DYNAMIC: IT RESPONDS TO AN INPUT BY UNDERGOING A TRANSIENT
RESPONSE BEFORE REACHING A STEADY-STATE RESPONSE THAT GENERALLY RESEMBLES THE INPUT. WE
HAVE ALREADY IDENTIFIED THESE TWO RESPONSES AND CITED A POSITION CONTROL SYSTEM (AN
ELEVATOR) AS AN EXAMPLE. IN THIS SECTION, WE DISCUSS THREE MAJOR OBJECTIVES OF SYSTEMS
ANALYSIS AND DESIGN: PRODUCING THE DESIRED TRANSIENT RESPONSE, REDUCING STEADY-STATE
ERROR, AND ACHIEVING STABILITY. WE ALSO ADDRESS SOME OTHER DESIGN CONCERNS, SUCH AS
COST AND THE SENSITIVITY OF SYSTEM PERFORMANCE TO CHANGES IN PARAMETERS.

12. TRANSIENT RESPONSE
• TRANSIENT RESPONSE IS IMPORTANT. IN THE CASE OF AN ELEVATOR, A SLOW
TRANSIENT RESPONSE MAKES PASSENGERS IMPATIENT, WHEREAS AN
EXCESSIVELY RAPID RESPONSE MAKES THEM UNCOMFORTABLE. IF THE
ELEVATOR OSCILLATES ABOUT THE ARRIVAL FLOOR FOR MORE THAN A
SECOND, A DISCONCERTING FEELING CAN RESULT. TRANSIENT RESPONSE IS
ALSO IMPORTANT FOR STRUCTURAL REASONS: TOO FAST A TRANSIENT
RESPONSE COULD CAUSE PERMANENT PHYSICAL DAMAGE.

13. STEADY-STATE RESPONSE
• ANOTHER ANALYSIS AND DESIGN GOAL FOCUSES ON THE STEADY-STATE RESPONSE. AS
WE HAVE SEEN, THIS RESPONSE RESEMBLES THE INPUT AND IS USUALLY WHAT REMAINS
AFTER THE TRANSIENTS HAVE DECAYED TO ZERO. FOR EXAMPLE, THIS RESPONSE MAY BE AN
ELEVATOR STOPPED NEAR THE FOURTH FLOOR OR THE HEAD OF A DISK DRIVE FINALLY
STOPPED AT THE CORRECT TRACK. WE ARE CONCERNED ABOUT THE ACCURACY OF THE
STEADY-STATE RESPONSE. AN ELEVATOR MUST BE LEVEL ENOUGH WITH THE FLOOR FOR
THE PASSENGERS TO EXIT, AND A READ/WRITE HEAD NOT POSITIONED OVER THE
COMMANDED TRACK RESULTS IN COMPUTER ERRORS. AN ANTENNA TRACKING A SATELLITE
MUST KEEP THE SATELLITE WELL WITHIN ITS BEAMWIDTH IN ORDER NOT TO LOSE TRACK. IN
THIS TEXT WE DEFINE STEADY-STATE ERRORS QUANTITATIVELY, ANALYZE A SYSTEM’S
STEADY-STATE ERROR, AND THEN DESIGN CORRECTIVE ACTION TO REDUCE THE STEADY-
STATE ERROR—OUR SECOND ANALYSIS AND DESIGN OBJECTIVE.

14. STABILITY
• STABILITY DISCUSSION OF TRANSIENT RESPONSE AND STEADY-STATE ERROR IS
MOOT IF THE SYSTEM DOES NOT HAVE STABILITY. IN ORDER TO EXPLAIN STABILITY,
WE START FROM THE FACT THAT THE TOTAL RESPONSE OF A SYSTEM IS THE SUM OF
THE NATURAL RESPONSE AND THE FORCED RESPONSE. WHEN YOU STUDIED
LINEAR DIFFERENTIAL EQUATIONS, YOU PROBABLY REFERRED TO THESE RESPONSES
AS THE HOMOGENEOUS AND THE PARTICULAR SOLUTIONS, RESPECTIVELY.
NATURAL RESPONSE DESCRIBES THE WAY THE SYSTEM DISSIPATES OR ACQUIRES
ENERGY. THE FORM OR NATURE OF THIS RESPONSE IS DEPENDENT ONLY ON THE
SYSTEM, NOT THE INPUT. ON THE OTHER HAND, THE FORM OR NATURE OF THE
FORCED RESPONSE IS DEPENDENT ON THE INPUT. THUS, FOR A LINEAR SYSTEM, WE
CAN WRITE
TOTAL RESPONSE = NATURAL RESPONSE + FORCED RESPONSE

15. • FOR A CONTROL SYSTEM TO BE USEFUL, THE NATURAL RESPONSE MUST (1)
EVENTUALLY APPROACH ZERO, THUS LEAVING ONLY THE FORCED RESPONSE, OR (2)
OSCILLATE. IN SOME SYSTEMS, HOWEVER, THE NATURAL RESPONSE GROWS
WITHOUT BOUND RATHER THAN DIMINISH TO ZERO OR OSCILLATE. EVENTUALLY,
THE NATURAL RESPONSE IS SO MUCH GREATER THAN THE FORCED RESPONSE THAT
THE SYSTEM IS NO LONGER CONTROLLED. THIS CONDITION, CALLED INSTABILITY,
COULD LEAD TO SELF-DESTRUCTION OF THE PHYSICAL DEVICE IF LIMIT STOPS ARE
NOT PART OF THE DESIGN. FOR EXAMPLE, THE ELEVATOR WOULD CRASH THROUGH
THE FLOOR OR EXIT THROUGH THE CEILING; AN AIRCRAFT WOULD GO INTO AN
UNCONTROLLABLE ROLL; OR AN ANTENNA COMMANDED TO POINT TO A TARGET
WOULD ROTATE, LINE UP WITH THE TARGET, BUT THEN BEGIN TO OSCILLATE ABOUT
THE TARGET WITH GROWING OSCILLATIONS AND INCREASING VELOCITY UNTIL
THE MOTOR OR AMPLIFIERS REACHED THEIR OUTPUT LIMITS OR UNTIL THE ANTENNA
WAS DAMAGED STRUCTURALLY.

16. • A TIME PLOT OF AN UNSTABLE SYSTEM WOULD SHOW A TRANSIENT RESPONSE
THAT GROWS WITHOUT BOUND AND WITHOUT ANY EVIDENCE OF A STEADY-STATE
RESPONSE. CONTROL SYSTEMS MUST BE DESIGNED TO BE STABLE. THAT IS, THEIR
NATURAL RESPONSE MUST DECAY TO ZERO AS TIME APPROACHES INFINITY, OR
OSCILLATE. IN MANY SYSTEMS THE TRANSIENT RESPONSE YOU SEE ON A TIME
RESPONSE PLOT CAN BE DIRECTLY RELATED TO THE NATURAL RESPONSE. THUS, IF
THE NATURAL RESPONSE DECAYS TO ZERO AS TIME APPROACHES INFINITY, THE
TRANSIENT RESPONSE WILL ALSO DIE OUT, LEAVING ONLY THE FORCED RESPONSE.
IF THE SYSTEM IS STABLE, THE PROPER TRANSIENT RESPONSE AND STEADY-STATE
ERROR CHARACTERISTICS CAN BE DESIGNED. STABILITY IS OUR THIRD ANALYSIS AND
DESIGN OBJECTIVE

17. THE DESIGN PROCESS